Book description
Introduction to Optimum Design is intended for use in a first course on engineering design and optimization. Virtually any problem for which specific parameters need to be determined to satisfy constraints can be formulated as a design optimization problem. The concepts and methods described in the text are quite general and applicable to all such formulations. Inasmuch, the range of application of the optimum design methodology is almost limitless, constrained only by the imagination and ingenuity of the user.Throughout the text, simple design problems involving two to three design variables and three to four constraints are solved in detail to illustrate fundamental concepts and basic ideas. The necessary results from optimization theory are stated and their implications are studied through application to engineering design problems. Theory and concepts of optimum design are explained only through examples and simple engineering applications. Several of the numerical procedures and concepts described in the text are useful in many other engineering courses and applications.
* Allows engineers involved in the design process to adapt optimum design concepts in their work using the material in the text.
* Basic concepts of optimality conditions and numerical methods are described with simple examples, making the material high teachable and learnable.
* Classroomtested for many years to attain optimum pedagogical effectiveness.
Table of contents
 Cover image
 Title page
 Table of Contents
 Copyright
 Jasbir S. Arora
 Dedication
 Preface
 Chapter 1: Introduction to Design

Chapter 2: Optimum Design Problem Formulation
 2.1: The Problem Formulation Process
 2.2: Design of a Can
 2.3: Insulated Spherical Tank Design
 2.4: Saw Mill Operation
 2.5: Design of a TwoBar Bracket
 2.6: Design of a Cabinet
 2.7: Minimum Weight Tubular Column Design
 2.8: Minimum Cost Cylindrical Tank Design
 2.9: Design of Coil Springs
 2.10: Minimum Weight Design of a Symmetric ThreeBar Truss
 2.11: A General Mathematical Model for Optimum Design
 Exercises for Chapter 2

Chapter 3: Graphical Optimization
 3.1: Graphical Solution Process
 3.2: Use of Mathematica for Graphical Optimization
 3.3: Use of MATLAB for Graphical Optimization
 3.4: Design Problem with Multiple Solutions
 3.5: Problem with Unbounded Solution
 3.6: Infeasible Problem
 3.7: Graphical Solution for Minimum Weight Tubular Column
 3.8: Graphical Solution for a Beam Design Problem
 Exercises for Chapter 3

Chapter 4: Optimum Design Concepts
 4.1: Definitions of Global and Local Minima
 4.2: Review of Some Basic Calculus Concepts
 4.3: Unconstrained Optimum Design Problems
 4.4: Constrained Optimum Design Problems
 4.5: Postoptimality Analysis: Physical Meaning of Lagrange Multipliers
 4.6: Global Optimality
 4.7: Engineering Design Examples
 Exercises for Chapter 4
 Chapter 5: More on Optimum Design Concepts

Chapter 6: Linear Programming Methods for Optimum Design
 6.1: Definition of a Standard Linear Programming Problem
 6.2: Basic Concepts Related to Linear Programming Problems
 6.3: Basic Ideas and Steps of the Simplex Method
 6.4: TwoPhase Simplex MethodArtificial Variables
 6.5: Postoptimality Analysis
 6.6: Solution of LP Problems Using Excel Solver
 Exercises for Chapter 6
 Chapter 7: More on Linear Programming Methods for Optimum Design
 Chapter 8: Numerical Methods for Unconstrained Optimum Design

Chapter 9: More on Numerical Methods for Unconstrained Optimum Design
 9.1: More on Step Size Determination
 9.2: More on Steepest Descent Method
 9.3: Scaling of Design Variables
 9.4: Search Direction Determination: Newton’s Method
 9.5: Search Direction Determination: QuasiNewton Methods
 9.6: Engineering Applications of Unconstrained Methods
 9.7: Solution of Constrained Problems Using Unconstrained Optimization Methods
 Exercises for Chapter 9*
 Chapter 10: Numerical Methods for Constrained Optimum Design

Chapter 11: More on Numerical Methods for Constrained Optimum Design
 11.1: Potential Constraint Strategy
 11.2: Quadratic Programming Problem
 11.2.1: Definition of QP Problem
 11.2.2: KKT Necessary Conditions for the QP Problem
 11.2.3: Transformation of KKT Conditions
 11.2.4: Simplex Method for Solving QP Problem
 11.3: Approximate Step Size Determination
 11.4: Constrained QuasiNewton Methods
 11.4.1: Derivation of Quadratic Programming Subproblem
 11.4.2: QuasiNewton Hessian Approximation
 11.4.3: Modified Constrained Steepest Descent Algorithm
 11.4.4: Observations on the Constrained QuasiNewton Methods
 11.4.5: Descent Functions
 11.5: Other Numerical Optimization Methods
 Chapter 12: Introduction to Optimum Design with MATLAB
 Chapter 13: Interactive Design Optimization

Chapter 14: Design Optimization Applications with Implicit Functions
 14.1: Formulation of Practical Design Optimization Problems
 14.2 Gradient Evaluation for Implicit Functions
 14.3: Issues in Practical Design Optimization
 14.4: Use of GeneralPurpose Software
 14.5: Optimum Design of a TwoMember Frame with OutofPlane Loads
 14.6: Optimum Design of a ThreeBar Structure for Multiple Performance Requirements
 14.7: Discrete Variable Optimum Design
 14.8: Optimal Control of Systems by Nonlinear Programming

Chapter 15: Discrete Variable Optimum Design Concepts and Methods
 15.1: Basic Concepts and Definitions
 15.2: Branch and Bound Methods (BBM)
 15.3: Integer Programming
 15.4: Sequential Linearization Methods
 15.5: Simulated Annealing
 15.6: Dynamic Roundingoff Method
 15.7: Neighborhood Search Method
 15.8: Methods for Linked Discrete Variables
 15.9: Selection of a Method
 Exercises for Chapter 15*
 Chapter 16: Genetic Algorithms for Optimum Design

Chapter 17: Multiobjective Optimum Design Concepts and Methods
 17.1: Problem Definition
 17.2: Terminology and Basic Concepts
 17.3: Multiobjective Genetic Algorithms
 17.4: Weighted Sum Method
 17.5: Weighted MinMax Method
 17.6: Weighted Global Criterion Method
 17.7: Lexicographic Method
 17.8: Bounded Objective Function Method
 17.9: Goal Programming
 17.10: Selection of Methods
 Exercises for Chapter 17
 Chapter 18: Global Optimization Concepts and Methods for Optimum Design
 Appendix A: Economic Analysis

Appendix B: Vector and Matrix Algebra
 B.1: Definition of Matrices
 B.2: Type of Matrices and Their Operations
 B.3: Solution of n Linear Equations in n Unknowns
 B.4: Solution of m Linear Equations in n Unknowns
 B.5: Concepts Related to a Set of Vectors
 B.6: Eigenvalues and Eigenvectors
 B.7*: Norm and Condition Number of a Matrix
 Exercises for Appendix B
 Appendix C: A Numerical Method for Solution of Nonlinear Equations
 Appendix D: Sample Computer Programs
 References
 Bibliography

Answers to Selected Problems
 Chapter 4: Optimum Design Concepts
 Chapter 5: More on Optimum Design Concepts
 Chapter 6: Linear Programming Methods for Optimum Design
 Chapter 7: More on Linear Programming Methods for Optimum Design
 Chapter 8: Numerical Methods for Unconstrained Optimum Design
 Chapter 9: More on Numerical Methods for Unconstrained Optimum Design 9.1
 Chapter 10: Numerical Methods for Constrained Optimum Design
 Chapter 12: Introduction to Optimum Design with MATLAB
 Chapter 13: Interactive Design Optimization
 Chapter 14: Design Optimization Applications with Implicit Functions
 Chapter 18: Global Optimization Concepts and Methods for Optimum Design 18.1
 Appendix A: Economic Analysis
 Appendix B: Vector and Matrix Algebra
 Appendix C: A Numerical Method for Solution of Nonlinear Equations
 Index
Product information
 Title: Introduction to Optimum Design, 2nd Edition
 Author(s):
 Release date: May 2004
 Publisher(s): Academic Press
 ISBN: 9780080470252
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